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Roychowdhury, Prasun; Suragan, Durvudkhan

Improvement of the discrete Hardy inequality. (English) Zbl 07900724

Bull. Sci. Math. 195, Article ID 103468, 12 p. (2024).
Summary: We establish a novel improvement of the classical discrete Hardy inequality, which gives the discrete version of a recent (continuous) inequality of R. L. Frank et al. [J. Math. Sci., New York 268, No. 3, 323–342 (2022; Zbl 1522.26015); translation from Probl. Mat. Anal. 118, 69–86 (2022)]. Our arguments build on certain weighted inequalities based on discrete analogues of symmetric decreasing rearrangement techniques.

MSC:

26D15 Inequalities for sums, series and integrals

Keywords:

discrete Hardy inequality; sharp constant; difference operator; uncertainty principle of discrete datum

Citations:

Zbl 1522.26015
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Full Text: DOI arXiv

References:

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